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Register a new userEfficient Method for Quantum Number Projection and Its Application to Tetrahedral Nuclear States
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We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying the method, we have microscopically calculated, for the first time, the energy spectra based on the exotic tetrahedral deformation in $^{108,110}$Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, $alpha_{32} gtsim 0.25$, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for $alpha_{32}approx 0.1-0.2$
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We have recently developed an efficient method of performing the full quantum number projection from the most general mean-field (HFB type) wave functions including the angular momentum, parity as well as the proton and neutron particle numbers. With this method, we have been investigating several nuclear structure mechanisms. In this report, we discuss the obtained quantum rotational spectra of the tetrahedral nuclear states formulating certain experimentally verifiable criteria, of the high-spin states, focussing on the wobbling- and chiral-bands, and of the drip-line nuclei as illustrative examples.
We discuss an extension of the generator coordinate method (GCM) by taking simultaneously a collective coordinate and its conjugate momentum as generator coordinates. To this end, we follow the idea of the dynamical GCM (DGCM) proposed by Goeke and Reinhard. We first show that the DGCM method can be regarded as an extension of the double projection method for the center of mass motion. As an application of DGCM, we then investigate the particle number projection, for which we not only carry out an integral over the gauge angle as in the usual particle number projection but also take a linear superposition of BCS states which have different mean particle numbers. We show that the ground state energy is significantly lowered by such effect, especially for magic nuclei for which the pairing gap is zero in the BCS approximation. This suggests that the present method makes a good alternative to the variation after projection (VAP) method, as the method is much simpler than the VAP.
We apply a new calculation scheme of a finite element method (FEM) for solving an elliptic boundary-value problem describing a quadrupole vibration collective nuclear model with tetrahedral symmetry. We use of shape functions constructed with interpolation Lagrange polynomials on a triangle finite element grid and compare the FEM results with obtained early by a finite difference method.
A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from the single-particle occupation probability. Either standard BCS or Lipkin-Nogami probability distributions can be used, thus the method is applicable for any pairing strength. The accuracy of the method is tested in the computation of pairing energies of model and real systems.
A new theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei. The method utilizes the equation-of-motion of the Gaussian wave packets to generate the basis wave functions having various cluster configurations. The generated basis wave functions are superposed to diagonalize the Hamiltonian. In other words, this method uses the real time as the generator coordinate. The application to the $3alpha$ system as a benchmark shows that the new method works efficiently and yields the result consistent with or better than the other cluster models. Brief discussion on the structure of the excited $0^+$ and $1^-$ states is also made.
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